效应代数的局部E-自同构
Local E-Automorphisms on Effect Algebras
摘要: 本文证明了维数大于等于3的可分Hilbert空间H的效应代数E(H)上的每个满的2-局部E-自同构是E-自同构以及Jordan代数Bs(H)上线性满的2-局部E-自同构是Jordan自同构,并且都具有的形式,其中U是酉算子或反酉算子。
Abstract:
In this paper, it is proved that each surjective two local E-automorphism on effect algebras E(H) of Hilbert space H which dimension is equal to or more than three is E-automorphism and each surjective and linear two local E-automorphism on real space Bs(H) is not only a Jordan automorphism but also has the form , where U is unitary or anti-unitary operator.
参考文献
[1]
|
P. Busch, M. Grabowski and P. J. Lahti. Operational quantum physics. Berlin-Heidelberg-New York: Springer-Verlag, 1995.
|
[2]
|
K. Kraus. State, effects and operations. Lecture Notes in Physics, Vol. 190. Berlin-Heidelberg-New York: Springer-Verlag, 1983.
|
[3]
|
L. Molnár. Local automorphisms of some quantum mechanical structures. Journal of Mathematical Physics, 2001, 58(2): 91-100.
|
[4]
|
R. V. Kadison. Local derivations. Journal of Algebra, 1990, 130(2): 494-509.
|
[5]
|
P. Semrl. Local automorphisms and derivations on B(H). Proceedings of the American Mathematical Society, 1997, 125(9): 183-193.
|
[6]
|
L. Molnár. Sequential isomorphismsbetween the sets of Von Neumann algebra effects. Acta Mathematica Scientia, 2003, 69(2-3): 755-772.
|
[7]
|
G. Ludwig. Fundation of quantum mechanics. Berlin: Springer Verlag, 1983.
|